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Oscillatory Integrals and Phenomena Beyond all Algebraic Orders

with Applications to Homoclinic Orbits in Reversible Systems

  • Book
  • © 2000

Overview

Authors:
  1. Eric Lombardi
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1741)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    • Eric Lombardi
    Pages 1-19

  3. "Exponential tools" for evaluating oscillatory integrals

    • Eric Lombardi
    Pages 22-76

  4. Resonances of reversible vector fields

    • Eric Lombardi
    Pages 78-100

  5. Analytic description of periodic orbits bifurcating from a pair of simple purely imaginary eigenvalues

    • Eric Lombardi
    Pages 101-122

  6. Constructive floquet theory for periodic matrices near a constant one

    • Eric Lombardi
    Pages 123-134

  7. Inversion of affine equations around reversible homoclinic connections

    • Eric Lombardi
    Pages 135-184

  8. The 02+iω resonance

    • Eric Lombardi
    Pages 186-325

  9. The 02+iω resonance in infinite dimensions. Application to water waves

    • Eric Lombardi
    Pages 327-357

  10. The (iω0)2iω1 resonance

    • Eric Lombardi
    Pages 359-403

  11. Back Matter

    Pages 405-413
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Keywords

About this book

During the last two decades, in several branches of science (water waves, crystal growth, travelling waves in one dimensional lattices, splitting of separatrices,...) different problems appeared in which the key point is the computation of exponentially small terms. This self-contained monograph gives new and rigorous mathematical tools which enable a systematic study of such problems. Starting with elementary illuminating examples, the book contains (i) new asymptotical tools for obtaining exponentially small equivalents of oscillatory integrals involving solutions of nonlinear differential equations; (ii) implementation of these tools for solving old open problems of bifurcation theory such as existence of homoclinic connections near resonances in reversible systems.

Bibliographic Information

  • Book Title: Oscillatory Integrals and Phenomena Beyond all Algebraic Orders

  • Book Subtitle: with Applications to Homoclinic Orbits in Reversible Systems

  • Authors: Eric Lombardi

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0104102

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-67785-7Published: 28 August 2000

  • eBook ISBN: 978-3-540-44971-3Published: 06 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 418

  • Topics: Analysis, Complex Systems, Statistical Physics and Dynamical Systems

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